How do use one channel from an image in a material?
You already have the image UV mapped to your mesh, good.
For the cycles render engine:
First you will want to make an entirely new material. (the settings from BI could mess things up a bit)
You want your new material's nodes to look something like this.

The first two nodes are how the texture gets in to your material.
The selected (Separate RGB) node is where it all happens, it takes the color form your image, and splits it into the three channels (the three outputs R G B). So since you only are interested in the blue channel, just plug that output in to your shader.

For the blender internal:
The process is much the same, you have to use the nodes. Here is what just the BI's material nodes look like. (This is assuming you already have the proper material and texture set up.)

Still just the Separate RGB node, and you are choosing what channel you want to use in the output.